Mathematics

Evaluate:
$$\displaystyle\int{\dfrac{{x}^{2}}{1+{x}^{3}}}dx$$


SOLUTION
$$\begin{array}{l}\text { Let } 1+x^{3}=z \\\quad \Rightarrow 3 x^{2} d x=d z \quad \Rightarrow x^{2} \mathrm{d} x=\dfrac{d z}{3} \\\therefore \quad \displaystyle  \int \dfrac{x^{2}}{1+x^{3}} \mathrm{d} \mathbf{x}\\=\dfrac{1}{3} \displaystyle \int \dfrac{\mathrm{d} z}{z}\\=\dfrac{1}{3} \log |z|+C\\=\dfrac{1}{3} \log \left|1+x^{3}\right|+C\end{array}$$
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Subjective Medium Published on 17th 09, 2020
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